Normal lattice of certain metabelian p-groups G with \(G/G^\prime\simeq (p,p)\)
arXiv:1403.3902
Abstract
Let p be an odd prime. The lattice of all normal subgroups and the terms of the lower and upper central series are determined for all metabelian p-groups with generator rank d=2 having abelianization of type (p,p) and minimal defect of commutativity k=0. It is shown that many of these groups are realized as Galois groups of second Hilbert p-class fields of an extensive set of quadratic fields which are characterized by principalization types of p-classes.
8 pages, 4 figures, presented at the conference Groups St Andrews 2013, University of St Andrews, Fife, Scotland, 9 August 2013